In current industrial applications many engineering parts are made of hard materials including dies, mold cavities and aerospace parts. Manufacturing these types of parts is classified as pocket milling. By using the regular machining methods, pocket milling takes a long time accompanied by high cost. Plunge milling, is a new machining strategy that has proven to have an excellent performance in the rough machining of hard materials. In plunge milling, the cutter is fed in the direction of the spindle axis, with the highest structural rigidity which showed a very interesting performance in removing the excess material rapidly in the rough operations. Mainly, according to the previous researchers, two directions are adopted to improve the efficiency of the plunge milling process. First, to reduce the cutting forces and increase chatter stability which attracts the majority of the researchers. Second, to optimize the tool path planning which has less attention.

Therefore, in the first part of the research, a new practical approach is established in optimized procedures to generate the tool paths for plunge milling of pockets, even for these with free-form boundaries and islands. This innovative approach is proposed as follows:​ (1) fill a pocket with minimum number of specified radii circles which are tangent to each other and/or the pocket boundary without overlapping by building an algorithm using the maximum hole degree (MHD) theory for solving the circle packing problem. (2) cover the areas left between the non-overlapped circles by the same used specified radii. Finally, solve the travelling sales man problem (TSP) for the circles with the same radii by using the simulated annealing algorithm. According to the results, this approach significantly advances the tool path planning technique for pockets plunge milling.

In the second part of the research, a new algorithm is proposed to calculate the global solution for constraint polynomial functions by using subtractive clustering which makes the results more accurate and faster to be obtained. This part is extremely useful to calculate the depth of cut for each plunging place in case of having a polynomial surface as a bottom of the machined pocket with high accuracy, and less calculation time to avoid gauging between the tool and the bottom surface.

The polynomial function can be classified according to the number of variables. In the proposed research, the functions with one and two variables have more importance because they graphically represent curves and surfaces which are the cases under study. Since the polynomial function under study can be represented graphically according to the number of the variables, the change in the function’s shape can be detected by the feature recognition. The feature recognition is done for the function’s shape by calculating the surface or curve curvature at the data points. The main procedure is;​ (1) identifying the entire features of the objective function which are classified according to the curvature as convex, concave, plane, and hyperbolic, (2) applying the sub-clustering technique for convex and concave regions to find the approximated centers of these regions, and eventually, (3) the clusters’ centers are calculated and used as initial points for local optimization technique which gives the local critical point for each region. The local minima are calculated, the global minimum is the minimum of the local minima.